16. Find the complete integrals of the foiowing equations: (i) z pq = p+4 che (i) p°q² +x?y? = x°q? (² + y?). (ii) 2.2 --lote intearal af"

Q: Evaluate the integral: ² ls teu du ds dt 0

A: We need to evaluate the following triple integral ∫12∫tt2∫0lnsteudu ds dt

Q: S, (3x² – 3yz + 2xz)dx + (3y² – 3xz + z²)dy + (3z² – 3xy + x² + 2yz)dz Calculate the curvilinear…

A: Let's find.

Q: (3, 1) (у? + 2ху) dx + (- 1, 2) (x² 2ху) dy +

A: We have to show that the curvilinear integral is independent of path and we have to find its…

Q: 1- Use trapezium's Rule with n = 4 to approximate the integral Vx dx

A: We have to use formula of Trapezoid Rule.

Q: 14 Find the integrals using integration by parts. a. Jx(x+ 4) dx b. JVF In Vrdx c. fr'e"dx d. [ (In…

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Q: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: Show that ∫0∞ e-x 2 dx = ∫10√(-ln y)  dy  by interpreting theintegrals as areas.

A:

Q: Evaluate the integral (12x + 12y)dx + (9x - y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

A:

Q: dr a) find possibce non-constant fonctron fr) for the mdetinite integral to be eralvaled by…

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Q: Ssin (y)cos(y)/3+ sin° (y) + 5e" dy

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Q: 14 Find the integrals using integration by parts. b. JF In /rdx In a. fx(x + 4)°dx c. fr'e"dx d.…

A: Just multiply by 1and go ahead.

Q: show that the differential forms in the integrals are exact. Then evaluate the integrals.

A:

Q: 1 8y² = x² – x* , 5x< curve segment is %D - rotated about the x-axis. Calculate the surface area of…

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Q: (3) Evaluate the line integral of the first type fez2 ds, where C: x = cost y = sint where 0 ≤ t ≤…

A: As per the company rule, we are supposed to solve one problem from a set of multiple problems.…

Q: Ue fe Einemial Theorem to ine tre coeficit ofnthe eparsion of ir+ 31

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Q: Set up an iterated triple integral equal to | = √√3 √3-x² √√30 x²+y² 3 √2-√4-x²-y² 2y dz dy dx…

A: The given problem is to set the given triple integral in Cartesian coordinates to convert into the…

Q: 3) S. (3x² – 3yz + 2xz)dx + (3y² – 3xz + z²)dy + (3z² – 3xy + x² + 2yz)dz - Calculate the…

A: Let's find.

Q: Exampley Consider the following nonlinear sine-Gordon equation Utt-Uxx+5 inu zo subject to the…

A: Solution: Given the Sine-Gordon equation utt-uxx+sinu=0   - - - - - (1) and initially conditions;…

Q: show that the differential forms in the integrals are exact. Then evaluate the integrals.

A: To Determine: show that the differential forms in the integrals are exact. Then evaluate the…

Q: 13. If u(x) = sin 3x and v(x) = x, what are du and dv? Writedown  u dv and  v du in this…

A: Given- ux=sin3x and vx=x To Find- The value of du and dv, write down the value of ∫udv and ∫vdu,…

Q: A// compute $(4+ e*) dx+ (siny + 3x*)dy Where c is closed bounded region lying in the first quarter…

A: See the attachment

Q: express the length of the curve as an integral but do not evaluate it. r = (2 − cos θ )−1, 0 ≤ θ ≤…

A: Definition used -                Length of the curve -            L=∫αβrθ2+r'(θ)2dθ

Q: Use the Fundamental Theorem of Line Integrals to calculate 7. di exactly. F6 sin(6x + y)i + sin(6x +…

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Q: Evaluate double integral 0 to 2, x to 2 2y^2 sinxy dydx

A: We have to integrate the double integral:

Q: Solve the equation by Cauchy's integral theorem. 1- dz 2- . 2z(4– z)dz

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: 3) . (3x2 — Зуz+ 2xz)dx + (3у? - 3xz + z?)dy + (372 — Зху + х? + 2yz)dz Calculate the curvilinear…

A: Let's find.

Q: Evaluate the integral / (8x + 3y)dx + (18x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A: Explanation of the solution is given below....

Q: 2 2 solid lying inside of the sphere, x+y² +z² = 16 , and inside the cylinder %D ll limits of…

A: An iterated triple integral in spherical coordinates to find the volume of the solid lying inside of…

Q: To find the arclength of y = 3x² + 3 from æ = 0 to x = 4, which is the correct integral? OL = | VI+…

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Q: show that uuX)-X (1+x*J% I'sasolutionto integralequation ux)=X-sinh (x-t)u (t) dt

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Q: and sk-X d the orea | between the curves

A: There is no area bounded by these two curves. but if we think at infinity they may be same. if we…

Q: 2. u(x)= secx+à So u(t)dt.

A: Given integral Fredholm equation, ux=sec2x+λ∫01utdt To find the solution of this equation.

Q: 1. Estimate the integral using Trapezoidal approximation rule with n=4: 2 + t)dt

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Q: Evaluate the integrals below: etanx sec² x 3. a) V(1 – (elanx )2 :. dx, b) / cot5x. dy

A: We need to integrate of the following integrals.

Q: 2π 3 [³* sin(y) + sec² (y) dy

A: We have to evaluate the given integral.

Q: Given: J Vx sinh TV

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Q: 64 ans: su 3 6. Calculate the area between the Curve fcx) = x²³²_4 and the lines y=2x + 4 and y=0,…

A: area between curve

Q: Find uhe integral y+ 2 dy

A: Substitute u=y+2,du=dy.  Note that y=u-2.

Q: 3) S. (3x² – 3yz + 2xz)dx + (3y² – 3xz + z²)dy + (3z² – 3xy + x² + 2yz)dz Calculate the curvilinear…

A: Let's find.

Q: 9 Set up an integral for the length of the Curve, yこx,05x<ト

A:

Q: Evaluate the line integral (4х + 5у)dx + (За — 6у)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: 3. Change the order of integration sin dydx. Hence, evaluate the integral. y

A: Sol ∫0π∫xπsinyydydxChange order of integration =∫0π∫0ysinyydxdy

Q: dt cos°(2 sin" 21)/1– 4r cos(2 sin2t

A:

Q: I+tgX dx; 2 COS X cos

A: Given: ∫1+tanxcos2xdx

Q: 2. Estimate the integral using Simpson's approximation rule with n=4: sin t dt

A: To estimate:∫0πsint dtn=4

Q: show that the differential forms in the integrals are exact. Then evaluate the integrals.

A: Here, we have   Assume ∫(0,0,0)(2,3,-6)2xdx+2ydy+2zdz                   (i)   Using the formula,…

Q: Evaluate the integral / (8x + 18y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A: We have to find value of given Integral along given Curve.

Q: Find the liner Jeneral integral of differential equations. ) (xy' -1) Int=24

A: Given: